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%I A202331 #8 May 27 2018 14:42:42
%S A202331 49,129,289,576,1052,1796,2906,4501,6723,9739,13743,18958,25638,34070,
%T A202331 44576,57515,73285,92325,115117,142188,174112,211512,255062,305489,
%U A202331 363575,430159,506139,592474,690186,800362,924156,1062791,1217561
%N A202331 Number of (n+1) X 5 binary arrays with consecutive windows of two bits considered as a binary number nondecreasing in every row and column.
%C A202331 Column 4 of A202335.
%H A202331 R. H. Hardin, <a href="/A202331/b202331.txt">Table of n, a(n) for n = 1..210</a>
%F A202331 Empirical: a(n) = (1/60)*n^5 + (3/8)*n^4 + 3*n^3 + (89/8)*n^2 + (1169/60)*n + 15.
%F A202331 Conjectures from _Colin Barker_, May 27 2018: (Start)
%F A202331 G.f.: x*(49 - 165*x + 250*x^2 - 203*x^3 + 86*x^4 - 15*x^5) / (1 - x)^6.
%F A202331 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F A202331 (End)
%e A202331 Some solutions for n=5:
%e A202331 ..0..0..0..0..0....0..0..0..0..0....0..0..0..1..0....0..0..0..0..0
%e A202331 ..0..0..0..1..0....0..0..0..0..0....0..0..0..1..0....0..0..0..0..0
%e A202331 ..0..0..0..1..0....0..0..0..0..0....0..0..0..1..1....0..0..0..1..0
%e A202331 ..0..0..0..1..0....0..0..0..1..1....0..0..0..1..1....0..0..1..1..1
%e A202331 ..0..1..1..1..1....0..0..0..1..1....1..1..1..1..1....1..1..1..1..1
%e A202331 ..0..0..0..1..1....0..0..1..1..1....0..0..1..1..1....1..1..1..1..1
%Y A202331 Cf. A202335.
%K A202331 nonn
%O A202331 1,1
%A A202331 _R. H. Hardin_, Dec 17 2011

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